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2009
Springer

On the Complexity of Matroid Isomorphism Problems

9 years 6 months ago
On the Complexity of Matroid Isomorphism Problems
We study the complexity of testing if two given matroids are isomorphic. The problem is easily seen to be in Σp 2 . In the case of linear matroids, which are represented over polynomially growing fields, we note that the problem is unlikely to be Σp 2 -complete and is coNPhard. We show that when the rank of the matroid is bounded by a constant, linear matroid isomorphism and matroid isomorphism are both polynomial time many-one equivalent to graph isomorphism. We give a polynomial time Turing reduction from graphic matroid isomorphism problem to the graph isomorphism problem. We then give a polynomial time many-one reduction from bounded rank matroid isomorphism problem to graphic matroid isomorphism, thus showing that all the above problems are polynomial time equivalent. Further, for linear and graphic matroids, we prove that the automorphism problem is polynomial time equivalent to the corresponding isomorphism problems. In addition, we give a polynomial time membership test algo...
B. V. Raghavendra Rao, Jayalal M. N. Sarma
Added 26 May 2010
Updated 26 May 2010
Type Conference
Year 2009
Where CSR
Authors B. V. Raghavendra Rao, Jayalal M. N. Sarma
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